US20060276215A1

US20060276215A1 - Method of allocating power over channels of a communication system

Info

Publication number: US20060276215A1
Application number: US11/141,065
Authority: US
Inventors: Angel Lozano; Antonia Tulino; Sergio Verdu
Original assignee: Lucent Technologies Inc
Current assignee: Nokia of America Corp
Priority date: 2005-06-01
Filing date: 2005-06-01
Publication date: 2006-12-07
Also published as: US7489944B2

Abstract

In one embodiment, the power for transmitting signals over at least one of a plurality of parallel channels is allocated based on a channel strength threshold and an estimated channel strength for the at least one channel. Here, the channel strength threshold is based on the estimated channel strengths for the plurality of channels.

Description

BACKGROUND OF THE INVENTION

1. Field of the Invention
The present invention related to communication, and provides methods for allocating transmission power over channels.
2. Description of Related Art
A problem often encountered in communication, either wireline or wireless, is that of allocating power over a set of parallel non-interacting channels sharing a common transmitter.
Although diverse criteria can be used in order to decide which fraction of the available power is allocated to each of the channels, a particularly enticing one is the maximization of the sum mutual information, which specifies the largest data rate per unit bandwidth that can be conveyed with arbitrary reliability. In the case that the noise impairing the communication is Gaussian, the mutual information is maximized if the transmitted signals are also Gaussian and the power is allocated over the available orthogonal channels according to the well-known waterfill policy.
Despite their optimality, however, Gaussian signals can never be realized in practice because of their infinite and continuous support. Rather, in actual communication systems the signals are modulated using discrete constellations. No solution is known for the power allocation over parallel channels that maximizes the mutual information when the transmitted signals are not Gaussian, and the waterfill policy is often invoked for non-Gaussian signals even though it is no longer optimal in that case.

SUMMARY OF THE INVENTION

The present invention related to communication, and provides methods for allocating transmission power over parallel channels.
In one embodiment, the power for transmitting a signal over at least one of a plurality of channels is allocated based on a channel strength threshold and an estimated channel strength for the at least one channel. Here, the channel strength threshold is based on the estimated channel strengths for the plurality of channels.
In another embodiment, the allocating step allocates power over each of the plurality of channels, and for each channel, the allocating step allocates power based on the channel threshold and the estimated channel strengths for the channels.
In another embodiment, the plurality of channels may be non-interacting parallel channels, and the signals transmitted over at least a portion of the channels may be non-Gaussian.
In one embodiment, the channel strength threshold may be calculated based on the estimated channel strengths for the plurality of channels and an average power available for transmission over the plurality of channels. In another embodiment, the channel strength threshold may be accessed from a memory.
In one embodiment, the estimated channel strength for at least one channel is a normalized representation of a signal-to-noise ratio on the channel.
In one embodiment, the allocating step allocates zero power to a channel in the plurality of channels if the estimated channel strength associated with the channel is less than or equal to the channel strength threshold.
In a further embodiment, the allocating step allocates a non-zero power to a channel in the plurality of channels based on the estimated channel strength for the channel if the estimated channel strength for the channel is greater than the channel strength threshold.
In yet a further embodiment, powers are allocated to a plurality of parallel non-interacting channels such that summutual information over the parallel non-interacting channels is maximized.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become more fully understood from the detailed description given herein below and the accompanying drawings which are given by way of illustration only, wherein like reference numerals designate corresponding parts in the various drawings, and wherein:
FIG. 1 illustrates a graphical representation of n parallel non-interacting channels; and
FIG. 2 illustrates an example apparatus embodiment implementing an embodiment of the method for allocating powers according to the present invention.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

For the purposes of explanation, a framework for explaining the embodiments of the present invention will be initially provided.
Consider a set of n parallel non-interacting channels as shown in FIG. 1. On the j-th such channel, the input-output relationship is:
y _j =h _j x _j +v _j (1)
where y_irepresents the received signal, x_jrepresents the transmitted signal, h_jis a scalar coefficient that represents the gain of the channel, and v_jrepresents the noise on the channel. The noise is zero-mean and Gaussian with variance:
E[|v _j|²]=σ_j ² (2)
The input x_jhas arbitrary distribution with power:
E[|x _j|² ]=p _j (3)
where E[·] is the expected value, and p_jis the power at which the transmitted signal x_jis transmitted over the channel.
Since the n channels are non-interacting, the noise is independent across channels and thus,
E[v_jv_l*]=0 j≠l (4)
where * denotes the complex conjugate.
The j-th input may be expressed as a unit-power signal s_j, whose format defines the corresponding modulation scheme, scaled as:
x _j =√{square root over (p _j )} s _j (5)
For convenience, a normalized representation of the signal-to-noise ratio may be defined for each channel as: $\begin{matrix} γ_{j} = \frac{{\langle h_{j} \rangle}^{2}}{σ_{j}^{2}} & (6) \end{matrix}$
which is a measure or estimate of the strength of that channel. The signal-to-noise ratio at the output of the j-th channel is given by p_jγ_j. For the purposes of explanation only, coherent communication, where the complex channel gains h₁, . . . , h_nare estimated and tracked by the receiver, for example, through the transmission of known pilot symbols, is assumed.
Given this framework, according to at least one embodiment of the present invention, a determination is made for the set of powers p₁, p₂, . . . , p_nsuch that the aggregate mutual information is satisfied subject to the constraint: $\begin{matrix} \frac{1}{n} \sum_{ℓ = 1}^{n} p_{ℓ} \leq P_{avg} & (7) \end{matrix}$
where P_avgis the average power available for transmission (determined by design parameters such as the size of the amplifiers, the batteries or power supply, etc. known in the art).
Before discussing the determination of the set of powers p₁, p₂, . . . , p_n, the MMMSE (minimum mean-square error) incurred on the estimation of the signals s₁, . . . , s_nwill be described to provide a better understanding of the embodiments of the present invention. The estimate of s_jthat minimizes the mean-square error is known to be the conditional mean estimator, where the estimate is given by:
ŝ _j =E[s _j |y _j] (8)
which is in general a nonlinear estimator. (It becomes linear in the special case that s_jis Gaussian.) The MMSE is then:
MMSE _j(p _jγ_j)=E[|s _j −ŝ _j|²] (9)
which is a function of the product p_jγ_j.

EXAMPLE EMBODIMENTS

In view of the above, the power allocation methodology according to one embodiment is provided by:
p_j=0 γ_j≦η
γ_j MMSE _j(p _jγ_j)=ηγ_j>η (10)
where η is a channel strength threshold having a value such that equation (7) is satisfied with strict equality. The set of powers satisfying these conditions maximizes the aggregate mutual information over the n channels.
Denoting by MMSE⁻¹(·) the inverse of MMSE(·) with respect to the composition of functions, equation (10) may be recast as: $\begin{matrix} \begin{matrix} p_{j} = 0 & γ_{j} \leq η \\ p_{j} = \frac{1}{γ_{j}} {MMSE}_{j}^{- 1} (\min {1, η / γ_{j}}) & γ_{j} > η \end{matrix} & (11) \end{matrix}$
with η being a solution to the nonlinear equation: $\begin{matrix} \sum_{j = 1}^{n} \frac{{MMSE}_{j}^{- 1} (\min {1, η / γ_{j}})}{n γ_{j}} = P_{avg} & (12) \end{matrix}$
When implemented, the gain h_jand variance σ_jfor each received signal y_jare estimated according to any well-known process. For example, techniques for estimating these values based on the pilot symbols in the received signal y_jare very well-known and in use today. For each channel j, the strength is estimated using the gain h_jand the variance σ_jaccording to equation (6). Using the estimated channel strengths and the average power available for transmission (i.e., P_avg), the channel strength threshold η is determined according to equation (12). Then, the powers p_jare then allocated according to equation (11). The allocated powers are then fed back to the transmitter.
FIG. 2 illustrates an example apparatus embodiment implementing this embodiment of the method for allocating powers according to the present invention. As shown, data parsers 10 parse the pilot signals from the respectively received signals y₁. . . y_n, and send the pilot signals to respective channel strength estimators 12. The channel strength estimators 12 estimate the respective gain h_jand variance σ_jof the channel over which the signal was received, and estimate the channel strength according to equation (6). Each of the channel strength estimates γ_jare fed to a power allocator 14, which also stores the average power available for transmitting over the channels. The power allocator 14 determines the channel strength threshold η according to equation (12), and then performs the power allocation according to equation (11). The power allocator 14 feeds back the power allocations to the transmitter. FIG. 2 also shows that the parsers 10 parse out the payload data from the received signals to respective receiver elements 16 for generating output. As will be appreciated, the elements of FIG. 2 may be implemented as a CPU, ASIC, FPGA, etc., or combination thereof at the receiver.
In alternative embodiments of the method and apparatus, the gain and variance values may be fed back to the transmitter, and the transmitter may perform the remainder of the embodiment for allocating powers. As yet another alternative, the estimated channel strengths may be fed back, and the transmitter may perform the remainder of the embodiment for allocating powers.
For n→∞, we can view the set {γ_j}, ∀j, as realizations of a random variable γ whose distribution describes the statistics of a fading channel. If this channel is stationary and ergodic, then η becomes the solution to: $\begin{matrix} E [\frac{{MSE}_{i}^{- 1} (\min {1, η / γ_{j}})}{γ}] = P_{avg} & (13) \end{matrix}$
with the expectation taken over γ. Thus, η depends only on the distribution of the fading channel, on P_avg, and on the format of the inputs. Parameterized by these quantities, η may be pre-computed and stored in memory for retrieval at the time of use.
The power allocation method according to the present invention applies to a wide range of communication problems. These include, but are not limited to:

- Multicarrier communication, where transmission takes places over several non-overlapping frequency bands. Each of these bands constitutes a channel. Typically, a sum power constraint is in place.
- OFDM (orthogonal frequency-division multiplexing), where transmission takes places over several overlapping frequency bands. The spectral shape of the transmitted signals is designed such that despite the overlap, these signals are orthogonal and thus remain non-interacting. OFDM is widely used in wireline DSL (digital subscriber line), wireless audio and video broadcast, wireless LANs, etc. Typically, a sum power constraint is in place. If the number of bands is very large, then the model n→∞ may be a useful idealization and the constraint may be put on the average.
- Multi-antenna or MIMO (multiple-input multiple-output) communication, where multiple transmit and multiple receive antennas are employed. If the complex channel gains between these antennas are known by the transmitter, the left singular vectors of the resulting matrix can be used for signaling and the right singular vectors for reception. The result is a set of orthogonal (non-interacting) parallel channels. Usually the sum power is constrained.
- Time-varying channels subject to an average power constraint. When the gain of an individual channel varies over time, it can be seen as an infinite succession of parallel channels where each such channel is a symbol or group of symbols over which the gain remains constant. In this case, the idealization n→∞ may be used with an average power constraint.

The invention being thus described, it will be obvious that the same may be varied in many ways. Such variations are not to be regarded as a departure from the invention, and all such modifications are intended to be included within the scope of the invention.

Claims

1. A method for allocating transmission power, comprising:

allocating a power for transmitting a signal over at least one of a plurality of channels based on a channel strength threshold and an estimated channel strength for the at least one channel, the channel strength threshold being based on estimated channel strengths for the plurality of channels.

2. The method of claim 1, wherein the plurality of channels are non-interacting parallel channels.

3. The method of claim 1, wherein the allocating step allocates power over each of the plurality of channels, and for each channel, the allocating step allocates power based on the channel threshold and the estimated channel strength for the channel.

4. The method of claim 3, wherein the plurality of channels are non-interacting parallel channels and signals being transmitted over at least a portion of the plurality of channels are non-Gaussian.

5. The method of claim 4, further comprising:

calculating the channel strength threshold based on the estimated channel strengths for the plurality of channels and an average power available for transmission over the plurality of channels.

6. The method of claim 4, further comprising:

accessing the channel strength threshold from a memory.

7. The method of claim 4, further comprising:

estimating a channel strength for each of the plurality of channels.

8. The method of claim 7, wherein the estimated channel strength for at least one channel is a normalized representation of a signal-to-noise ratio on the channel.

9. The method of claim 4, wherein the allocating step allocates zero power to a channel in the plurality of channels if the estimated channel strength associated with the channel is less than or equal to the channel strength threshold.

10. The method of claim 9, wherein the allocating step allocates a non-zero power to a channel in the plurality of channels based on the estimated channel strength for the channel if the estimated channel strength for the channel is greater than the channel strength threshold.

11. The method of claim 10, wherein the allocating step allocates power to a channel j based on the following expression:

\begin{matrix} \begin{matrix} p_{j} = 0 & γ_{j} \leq η \\ p_{j} = \frac{1}{γ_{j}} {MMSE}_{j}^{- 1} (\min {1, η / γ_{j}}) & γ_{j} > η \end{matrix} & (11) \end{matrix}

where γ_jis the estimated channel strength of channel j, η is the channel strength threshold, and p_jis the allocated power for channel j.

12. The method of claim 11, wherein the channel strength threshold is determined according to the following expression:

\begin{matrix} \sum_{j = 1}^{n} \frac{{MMSE}_{j}^{- 1} (\min {1, η / γ_{j}})}{n γ_{j}} = P_{avg} & (12) \end{matrix}

where n is a number of the plurality of channels.

13. The method of claim 4, wherein the allocating step allocates a non-zero power to a channel in the plurality of channels based on the estimated channel strength for the channel if the estimated channel strength for the channel is greater than the channel strength threshold.

14. The method of claim 1, further comprising:

15. The method of claim 1, further comprising:

accessing the channel strength threshold from a memory.

16. The method of claim 1, wherein the estimated channel strength for the at least one channel is a normalized representation of a signal-to-noise ratio on the channel.

17. The method of claim 1, wherein the allocating step allocates zero power to the at least one channel if the estimated channel strength associated with the at least one channel is less than or equal to the channel strength threshold.

18. The method of claim 17, wherein the allocating step allocates a non-zero power to the at least one channel based on the estimated channel strength for the at least one channel if the estimated channel strength for the at least one channel is greater than the channel strength threshold.

19. The method of claim 1, wherein the allocating step allocates a non-zero power to the at least one channel based on the estimated channel strength for the at least one channel if the estimated channel strength for the at least one channel is greater than the channel strength threshold.

20. A method for allocating channel transmission power, comprising:

allocating powers to a plurality of parallel non-interacting channels that maximize sum mutual information over the plurality of parallel non-interacting channels.